Triple patterning lithography (TPL) has been recognized as one of the most promising techniques for 14/10nm technology node. In this paper, we applied triple patterning lithography on standard cell based designs, and proposed a novel algorithm to solve the problem. The algorithm guarantees to find a legal TPL decomposition with optimal number of stitches if one exists. A graph model is proposed to reduce the number of vertices in the solution graph, and a fast approach is developed to achieve simultaneous runtime and memory improvement. An efficient approach to limit the number of stitches is also proposed, which greatly reduces the total number of stitch candidates and enables an incremental implementation of the algorithm. Experimental results shows that the proposed algorithm is very efficient, which achieves 39.1% runtime improvement and 18.4% memory reduction compared with the state-of-the-art TPL algorithm on the same problem.

Directed Self-Assembly (DSA) is a promising technique for contacts/vias patterning, where groups of contacts/vias are patterned by guiding templates. As the templates are patterned by traditional lithography, their shapes may vary due to the process variations, which will ultimately affect the contacts/vias even for the same type of template. Due to the complexity of the DSA process, rigorous process simulation is unacceptably slow for full chip verification. This paper formulate several critical problems in DSA verification, and proposes a design automation methodology that consists of a data preparation and a model learning stage. We present a novel DSA model with Point Correspondence and Segment Distance features for robust learning. Following the methodology, we propose an effective machine learning (ML) based method for DSA hotspot detection. The results of our initial experiments have already demonstrated the high-efficiency of our ML-based approach with over 85% detection accuracy. Compared to the minutes or even hours of simulation time in rigorous method, the methodology in this paper validates the research potential along this direction.

Triple patterning lithography (TPL) has been recognized as one of the most promising techniques for 14/10nm technology node. There are various concerns for TPL decompositions. For standard cell based designs, assigning the same pattern for the same type of cells is a desired property for TPL decomposition. It is more robust for process variations and gives the chip similar physical and electrical characteristics as well as more reliable and predictable performance. Assigning the same type of pattern for the same type of cell is called a constrained pattern assignment (CPA) problem. In this paper, we integrated the flow of detailed placement and TPL decompositions with CPA coloring constraints. We focused on refining a layout to make it CPA-friendly during the detailed placement stage while minimizing the area and HPWL (half perimeter wire length) overhead. A weighted partial MAX SAT approach is proposed which guarantees to obtain a CPA-friendly detailed placement result while minimizing the area overhead. An efficient graph model is also proposed to compute the locations of the cells with optimal HPWL. Our formulation is very efficient and achieves a 79.4% area overhead reduction compared with the approach of fixing cell colors beforehand. Better HPWL are also achieved consistently over all benchmarks.

Triple patterning lithography (TPL) has been recognized as one of the most promising candidates for 14/10nm technology node. Apart from obtaining legal TPL decompositions, various concerns have been raised by the designers, among them consistently assigning the same pattern for the same type of standard cells and balancing the usage of the three masks are two most critical ones. In this paper, a hybrid approach (SAT followed by a sliding-window approach) is proposed targeting at these two problems. To assign the same pattern for the same type of standard cell, we pre-color the boundary polygons of each type of cell by solving a small SAT problem. Following that we propose a sliding-window based approach to compute a locally balanced decomposition. Our algorithm guarantees to find a feasible solution if one exists. Experimental results verify that the problem can be solved very efficiently with the proposed algorithm. Superior locally balanced decompositions are achieved compared with the previous approach in.

Self-aligned double patterning is one of the most promising double patterning techniques for sub-20nm nodes. As in any multiple patterning techniques, layout decomposition is the most important problem. In SADP decomposition, overlay is among the most primary concerns. Most of the existing works target at minimizing the overall overlay, while others totally forbid the overlay. On the other hand, most of the works either rely on exponential time methods, or apply heuristic that cannot guarantee to find a solution. In this paper, we consider the SADP decomposition problem in row-based standard cell layout, where the overlay violations are minimized. Although SADP decomposition has been shown to be NP-hard in general, we showed that it can be solved in polynomial time when the layout is row-based standard cells. We propose a polynomial time optimal algorithm that finds a decomposition with minimum overlay violations. The efficiency of our method is further demonstrated by the experimental results.

The significant mismatch between the objective of wirelength and routing congestion makes the routability issue even more important in placement. In this paper, we describe a routability-driven placer called Ripple. Each step, including global placement, legalization, and detailed placement, is made to trade-off between routability and wirelength. We propose a robust and effective flow by using cell inflation to relieve routing congestion. Cell inflation has traditionally been used to deal with congestion and we will discuss how this technique can be used easily and robustly in the global placement. Besides, unlike many previous works that focus on different types of swapping strategies, we analyze and propose some simple and effective approaches when considering routability in the legalization and detailed placement steps. Experimental results show that Ripple is particularly effective in improving routability. When compared to the top results in the ISPD 2011 Contest and SimPLR, Ripple can obtain the smallest overflow and half-perimeter wirelength on average, while the congestion hot spots are also distributed sparsely in Ripple.

Link based non-tree clock network is an effective and economic way to reduce clock skew caused by variations. However, it is still an open topic where links should be inserted in order to achieve largest skew reduction with smaller extra resources. We propose a new method using linear program to solve this problem in this paper. In our approach, clock skew in a non-tree clock network is computed using the delay model in [13] and the information is used to select the node pairs for link insertion. Tradeoff between crosslink length and skew reduction effect is explored. Based on the analysis, we propose a new algorithm to insert crosslinks into a clock network. We compare our work with the method in [1] and a recent work [4] which inserts links between internal nodes of a tree. Experiments show that our method can reduce skew under variations effectively.

As minimum feature size keeps shrinking, and the next generation lithography (e.g, EUV) further delays, double patterning lithography (DPL) has been widely recognized as a feasible lithography solution in 20nm technology node. However, as technology continues to scale to 14/10nm, DPL begins to show its limitations and usually generates too many undesirable stitches. Triple patterning lithography (TPL) is a natural extension of DPL to conquer the difficulties and achieve a stitch-free layout decomposition. In this paper, we study the standard cell based row-structure layout decomposition problem in TPL. Although the general TPL layout decomposition problem is NP-hard, in this paper we will show that for standard cell based TPL layout decomposition problem, it is polynomial time solvable. We propose a polynomial time algorithm to solve the problem optimally and our approach has the capability to find all stitch-free decompositions. Color balancing is also considered to ensure a balanced triple patterning decomposition. To speed up the algorithm, we further propose a hierarchical algorithm for standard cell based layout, which can reduce the run time by 34.5% on average without sacrificing the optimality. We also extend our algorithm to allow stitches for complex circuit designs, and our algorithm guarantees to find optimal solutions with minimum number of stitches.

Designing a high-quality clock network is very important in very large-scale integrated designs today, as it is the clock network that synchronizes all the elements of a chip, and it is also a major source of power dissipation of a system. Early study by Pham in 2006 shows that about 18.1% of the total clock capacitance was due to this postgrid clock routing (i.e., lower mesh wires plus clock twig wires). In this paper, we proposed a partition-based path expansion algorithm to solve this postgrid clock routing problem effectively. Experimental results on industrial test cases show that our algorithm can improve over the latest work by Shelar on this problem significantly by reducing the wire capacitance by 24.6% and the wirelength by 23.6%.

In this paper, we describe a routability-driven placer called Ripple. Two major techniques called cell inflation and net-based movement are used in global placement followed by a rough legalization step to reduce congestion. Cell inflation is performed in the horizontal and the vertical directions alternatively. We propose a new method called net-based movement, in which a target position is calculated for each cell by considering the movement of a net as a whole instead of working on each cell individually. In detailed placement, we use a combination of two kinds of strategy: the traditional HPWL-driven approach and our new congestion-driven approach. Experimental results show that Ripple is very effective in improving routability. Comparing with our pervious placer, which is the winner in the ISPD 2011 Contest, Ripple can further improve the overflow by 38% while reduce the runtime is reduced by 54%.

Clock distribution in VLSI designs is of crucial importance and it is also a major source of power dissipation of a system. For today's high performance microprocessors, clock signals are usually distributed by a global clock grid covering the whole chip, followed by post-grid routing that connects clock loads to the clock grid. Early study [2] shows that about 18.1% of the total clock capacitance dissipation was due to this post-grid clock routing (i.e., lower mesh wires plus clock twig wires). This post-grid clock routing problem is thus an important one but not many previous works have addressed it. In this paper, we try to solve this problem of connecting clock ports to the clock grid through reserved tracks on multiple metal layers, with delay and slew constraints. Note that a set of routing tracks are reserved for this grid-to-ports clock wires in practice because of the conventional modular design style of high-performance microprocessors. We propose a new expansion algorithm based on the heap data structure to solve the problem effectively. Experimental results on industrial test cases show that our algorithm can improve over the latest work on this problem [1] significantly by reducing the capacitance by 24.6% and the wire length by 23.6%. We also validate our results using hspice simulation. Finally, our approach is very efficient and for larger test cases with about 2000 ports, the runtime is in seconds.

Clock network construction is one key problem in high performance VLSI design. Reducing the clock skew variation is one of the most important objectives during clock network synthesis. Local clock skew (LCS) is the clock skew between any two sinks with distance less than or equal to a given threshold. It is defined in the ISPD 2010 High Performance Clock Network Synthesis Contest, and it is a novel criterion that captures process variation effects on a clock network. In this paper, we propose a hybrid method that creates a mesh upon a tree topology. Total wire and buffer capacitance is minimized under the LCS and slew constraints. In our method, a clock mesh will be built first according to the positions and capacitance of the sinks. A top-level tree is then built to drive the mesh. A blockage-aware routing method is used during the tree construction. Experimental results show our efficiency and the solution generated by our approach can satisfy the LCS constraint of all the benchmarks in the contest, with a fair capacitance usage.